Question: Solve for $x$ and $y$ using elimination. ${4x-6y = 2}$ ${2x+5y = 9}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the bottom equation by $-2$ ${4x-6y = 2}$ $-4x-10y = -18$ Add the top and bottom equations together. $-16y = -16$ $\dfrac{-16y}{{-16}} = \dfrac{-16}{{-16}}$ ${y = 1}$ Now that you know ${y = 1}$ , plug it back into $\thinspace {4x-6y = 2}\thinspace$ to find $x$ ${4x - 6}{(1)}{= 2}$ $4x-6 = 2$ $4x-6{+6} = 2{+6}$ $4x = 8$ $\dfrac{4x}{{4}} = \dfrac{8}{{4}}$ ${x = 2}$ You can also plug ${y = 1}$ into $\thinspace {2x+5y = 9}\thinspace$ and get the same answer for $x$ : ${2x + 5}{(1)}{= 9}$ ${x = 2}$